Ordering Numbers

Ordering Numbers

Comparing Two Numbers of the Same Length

When asked to put a group of numbers in to order of size you need to know the value of each digit in the number.

If you need to remind yourself what value each digit in a number has please take a look at the Place Value lesson.

Let’s compare these two numbers:

527 and 438

Both these numbers have three digits, so it is easy to see which is bigger. We just compare the first digit of each number which in this case is in the hundreds column:

527 and 438

We can see 527 is bigger as it has a 5 in the hundreds column where as 438 has a 4 in the same column.

How about ordering these two numbers:

3221 and 3389

In this case the numbers have the same number of digits and they have the same first digit in the thousands column (both have 3).

So we simply need to look at the next column along to the right and compare those digits.

In this case the next column is the hundreds column.

3221 and 3389

3389 has a 3 in the hundreds column where as 3221 has a 2.

So 3389 is the bigger number.

Here are two very similar numbers:

22471 and 22482

When comparing similar numbers you repeat the process of comparing digits moving right along the columns until you find one number with a bigger digit, and then you know this is the bigger number.

In this case we move all the way down to the the tens column where 22482 has an 8 and 22471 has a 7. So 22482 is the bigger number.

Ordering Several Numbers of the Same Length

When comparing more than two numbers that have the same number of digits, for example:

489, 423, 128 and 212.

You must take the first digit in each number and order the numbers according to this.

When 2 or more numbers have the same digit in a column you move on to the next digit and order the numbers according to this.

So with the numbers given above we can start by comparing their first digits and write them down in a list based on how big it is.

When numbers have the same first digit we can just write them in a group next to each other for now:

128, 212, 489, 423

The last two numbers both have 4 as their first digit, so we need to check the second digit to find their size order and rewrite the list with them in size order:

128, 212, 423, 489

Ordering Numbers of Different Lengths

When asked to compare whole numbers with a different number of digits, for example:

3449, 204, 12, 3299, 2288

You can tell straight away that the numbers with more digits are bigger than the numbers with less (when dealing with decimals this is not true but with whole numbers like we have here it is).

With the numbers above, the numbers with 4 digits are bigger than the ones with 3 and 2 digits as they have a digit in the thousands column. You can see also that the 3 digit number is bigger than the 2 digit number as it has a digit in the hundreds column.

So we can straight away roughly order the numbers based on the number of digits they have:

12, 204, (3449, 3299, 2288)

I have grouped some of the numbers in brackets as they have the same number of digits and have not yet been ordered amongst themselves but they are in the correct place as a group.

Next we can order the numbers in the group by comparing their first digits:

12, 204, (2288, 3449, 3299)

As two numbers have the same first digit we can order them by moving one column right and comparing the digits there:

12, 204, 2288, 3299, 3449

Important Symbols

When comparing the size of numbers there are three symbols that you need to understand:

=

<

>

The first one ‘=‘ is easy, it is the equals sign meaning that the values on either side of it are equal, for example:

10 + 4 = 14

‘<‘ means less than. The value on the left of the symbol is less than the value on the right.

For example 4 is ‘less than’ 10 looks like:

4 < 10

‘>’ means greater than. The value on the left is greater than the value on the right.

For example 12 is ‘greater than’ 3 looks like:

12 > 3

A good way to remember the difference between the two symbols ‘less than‘ and ‘greater than‘, is to look carefully at the shape of each symbol.

The ‘less than‘ symbol looks like this: < . It goes from a small point on the left to a big opening on the right. So we know the smaller value is on the left by the small point and it is ‘less than‘ the bigger value on the right by the big opening.

The ‘greater than‘ symbol is the opposite, it looks like this: > . It goes from a big opening on the left to a small point on the right. So we know the bigger value is on the left of the symbol next to the big opening and it is ‘greater than‘ the smaller value on the right by the small point.